Problems on Numbers Questions for the CAT are part of the Quantitative Aptitude Through Problems on Numbers questions, aspirants are tested to solve questions with fractions. The difficulty level of these questions is easy to moderate.

## What are some CAT Decimal Fraction Practice Questions?

**Q1. **What value will replace the question mark in the following equations?

(i) 5172.49 + 378.352 +? = 9318.678

(ii) ? – 7328.96 = 5169.38

**Answer 1. **(i) 3767.836

(ii) 12498.34

**Detailed Solution. **(i) Let 5172.49 + 378.352 + x = 9318.678.

Then, x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836.

(ii) Let x – 7328.96 = 5169.38. Then, x = 5169.38 + 7328.96 = 12498.34.

**Q2. **Find the products: (i) 6.3204 × 100 (ii) .069 × 10000

**Answer 2.** 690

**Detailed Solution. **(i) 6.3204 × 100 = 632.04. (ii) .069 × 10000 = .0690 × 10000 = 690.

**Q3. **Find the products:

(i) 2.1693 × 1.4

(ii) .4 × .04 × .004 × 40

(iii) 6.66 × 66.6 × 66

**Answer 3. **(i) 3.03702

(ii) .002560

(iii) 29274.696

**Detailed Solution. **(i) 21693 × 14 = 303702. Sum of decimal places = (4 + 1) = 5.

2.1693 × 1.4 = 3.03702.

(ii) 4 × 4 × 4 × 40 = 2560. Sum of decimal places = (1 + 2 + 3) = 6.

.4 × .04 × .004 × 40 = .002560.

(iii) 666 × 666 × 66 = 29274696. Sum of decimal places = (2 + 1) = 3.

6.66 × 66.6 × 66 = 29274.696.

**Q4.** Given that 268 × 74 = 19832, find the value of 2.68 × .74.

**Answer 4.** 1.9832

**Detailed Solution. **Sum of decimal places = (2 + 2) = 4.

∴ 2.68 × .74 = 1.9832.

## What are the must-do Decimal Fraction questions for the CAT exam?

**Q5. **Find the quotient:

(i) 0.63 ÷ 9

(ii) 0.0204 ÷ 17

(iii) 3.1603 ÷ 13

**Answer 5. **(i) .07

(ii) .0012

(iii) .2431

**Detailed Solution. **(i) 63 ÷ 9 = 7. Dividend contains 2 places of decimal.

∴ 0.63 ÷ 9 = .07.

(ii) 204 ÷ 17 = 12. Dividend contains 4 places of decimal.

∴ 0.0204 ÷ 17 = .0012.

(iii) 31603 ÷ 13 = 2431. Dividend contains 4 places of decimal.

∴ 3.1603 ÷ 13 = .2431.

**Q6. **Evaluate:

(i) 35 + .07

(ii) 2.5 + 0.0005

(iii) 136.09 + 43.9

**Answer 6. **(i) 500

(ii) 5000

(iii) 3.1

**Detailed Solution. **(i) 35/0.07 = (35 × 100) / (0.07 × 100) = 3500/7 = 500.

(ii) 2.5/0.0005 = (2.5 × 10000) / (0.0005 × 10000) = 25000/5 = 5000.

(iii) 136.09/43.9 = (136.09 × 10) / (43.9 × 10) = 1360.9/439 = 3.1.

**Q7.** What value will come in place of question mark in the following equations ?

(i) 0.006 ÷? = 0.6

(ii)? ÷ .025 = 80

**Answer 7. **(i) 0.01.

(ii) 2.

**Detailed Solution. **(i) 0.006/x = 0.6

Multiplying both sides by x: 0.006 = 0.6x

Dividing both sides by 0.6: x = 0.006/0.6 = 0.01

(ii) x/0.025 = 80

Multiplying both sides by 0.025: x = 80 × 0.025 = 2

**Q8. **If 1/3.718 = .2689, then find the value of 1/.0003718.

**Answer 8. **2689

**Detailed Solution.** 1/.0003718 = 10000/3.718 = (10000 x 1/3.178) = 10000 x .2689 = 2689

## What were the previous year's CAT Decimal Fraction questions?

**Q9. **Evaluate:

(i) 0.5 × 5.6 ÷ 0.5 × 12

(ii) 25 × 3.25 + 50.4 ÷ 24

(iii) 0.01 × 0.1 – 0.001 ÷ 10 + 0.01

(iv) 12.28 × 1.5 – 36 ÷ 2.4

**Answer 9. **(i) 67.2

(ii) 83.35

(iii) 0.0109

(iv) 3.42

**Detailed Solution. **(i) Given expression = 0.5 x (5.6/0.5) x 12 = 5x56x12/50 = 3360/72 = 67.2

(ii) Given expression = 25 x 3.25 + 50.4/24 = 81.25 + 2.1 = 83.35

(iii) Given expression = 0.001 - 0.01/10 + 0.01 = 0.001 - 0.0001 + 0.011 = 0.0109

(iv) Given expression = 12.28 x 1.5 - 36/2.4 = 18.42 - 15 = 3.42

**Q10. **Simplify.

(7/8) ÷ (5/6) × (3/4) + (1/3) × (2/5)

**Answer 10. **0.967.

**Detailed Solution.** Convert all fractions to their equivalent forms with a common denominator.

7/8 = 21/24

5/6 = 20/24

3/4 = 18/24

1/3 = 8/24

2/5 = 9.6/24 (converting 2/5 to 9.6/24 for ease of calculation)

Perform the operations following the order of BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

(21/24) ÷ (20/24) × (18/24) + (8/24) × (9.6/24)

= (21/20) × (18/24) + (8/24) × (9.6/24)

= 1.05 × 0.75 + 0.4

= 0.7875 + 0.4

= 1.1875

Express the result as a decimal fraction by dividing the numerator by the denominator.

1.1875 = 1.1875/1 = 0.967

**Q11. **Express the repeating decimal 0.27272727... as a fraction in its simplest form**.**

**Answer 11. **9/33

Detailed Solution. Let x = 0.27272727...

Step 1: Multiply the equation by 100 to remove the decimal point.

100x = 27.272727...

Step 2: Subtract the original equation from the new equation.

100x - x = 27.272727... - 0.27272727...

99x = 27

Step 3: Divide both sides by 99.

x = 27/99

Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

GCD of 27 and 99 is 3.

27/3 = 9

99/3 = 33

Therefore, the simplest fraction form of the repeating decimal 0.27272727... is 9/33.

**Q12. **(a) Express the repeating decimal 0.184184184... as a fraction in its simplest form.

(b) If the fraction obtained in part (a) is multiplied by 2/5, express the result as a decimal.

(c) Find the value of (0.184184184... + 2/5) correct to three decimal places.

**Answer 12**. (a) 4/27

(b) 0.059259259...

(c) 0.584

**Detailed Solution. **(a) Let x = 0.184184184...

Multiplying by 1000: 1000x = 184.184184...

Subtracting the original equation: 999x = 184

x = 184/999

Simplifying by dividing numerator and denominator by their GCD (37):

x = 4/27

(b) (4/27) × (2/5) = 8/135 = 0.059259259...

(c) 0.184184184... + 2/5 = 0.184184184... + 0.4

= 0.584184184...

= 0.584 (correct to three decimal places)

## What were the Decimal Fractions questions on the CAT 2022 exam?

**Q13. **Simplify:

(2.375 ÷ 1.25) × (0.64 ÷ 0.08) - (3.5 ÷ 0.25)

**Answer 13. **Option (A) 12.

**Detailed Solution. **Step 1: Simplify (2.375 ÷ 1.25)

2.375 ÷ 1.25 = 1.9

Step 2: Simplify (0.64 ÷ 0.08)

0.64 ÷ 0.08 = 8

Step 3: Simplify (3.5 ÷ 0.25)

3.5 ÷ 0.25 = 14

Step 4: Evaluate the expression

(1.9 × 8) - 14

= 15.2 - 14

= 1.2

**Q14. **Simplify :

(5.273 ÷ 0.014) + (7.685 ÷ 0.017) - (2.149 ÷ 0.023)

**Answer 14. **318.55

**Detailed Solution. **Convert decimals to fractions with denominator 2310

5.273 = 5273/2310

0.014 = 14/2310

7.685 = 7685/2310

0.017 = 17/2310

2.149 = 2149/2310

0.023 = 23/2310

Set up the expression with fractions

= (5273/14) + (7685/17) - (2149/23)

Convert fractions to equivalent fractions with common denominator of 2310

= (376,642/2310) + (452,647/2310) - (93,434/2310)

Perform operations

= 829,289/2310 - 93,434/2310

= 735,855/2310

Simplify the fraction

735,855/2310 = 318.55

**Q15. **Simplify :

(3.27 × 2.105) ÷ (0.63 × 1.4)

**Answer 15. **7.8

**Detailed Solution. **Multiply the numbers in the numerator and denominator separately.

3.27 × 2.105 = 6.88635

0.63 × 1.4 = 0.882

Divide the numerator by the denominator.

6.88635 ÷ 0.882 = 7.8

Therefore, the simplified value of the expression (3.27 × 2.105) ÷ (0.63 × 1.4) is 7.8.

**Q16. **Evaluate:

(5.28 ÷ 1.8) + (2.7 × 3.15) - (7.2 ÷ 0.9)

**Answer 16. **3.44

**Detailed Solution.** Perform the divisions first.

5.28 ÷ 1.8 = 2.93333...

7.2 ÷ 0.9 = 8

Perform the multiplication.

2.7 × 3.15 = 8.505

Perform the addition and subtraction in the given order.

2.93333... + 8.505 - 8 = 3.43833...

Therefore, the value of the expression (5.28 ÷ 1.8) + (2.7 × 3.15) - (7.2 ÷ 0.9) is approximately 3.44.

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